Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x+1}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{3x^3+x-11}{x+1}=$
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice that the expression in the numerator is missing a $2^{\text{nd}}$ degree term. To avoid any confusion, let's add that term as $0x^2$. $\begin{array}{r} 3x^2-3x+\phantom{1}4 \\ x+1|\overline{3x^3+0x^2+\phantom{3}x-11} \\ \mathllap{-(}\underline{3x^3+3x^2\phantom{+3x-11}\rlap )} \\ -3x^2+\phantom{0}x-11 \\ \mathllap{-(}\underline{-3x^2-3x\phantom{-11}\rlap )} \\ 4x-11 \\ \mathllap{-(}\underline{4x+\phantom{1}4\rlap )} \\ -15 \end{array}$ We found that the quotient is $3x^2-3x+4$ and the remainder is $-15$ : $\dfrac{3x^3+x-11}{x+1}=3x^2-3x+4-\dfrac{15}{x+1}$